All categories

3 years ago

1000 students participated in a survey on a university campus about their TV watching habits. All

1 answer:

5 0

Hi, you've asked an unclear question. However, I inferred you may want to know the actual number of students represented by the percentages of 27%, and 61%.

<u>Explanation:</u>

Finding percentage usually involves performing two operations; multiplication and division.

First, all (100%) of respondents said they watched TV at least at some point during the day.

Next, 27% of respondents stated that they only watched television during prime time hours, in which the actual number of students represented by the percentage is calculated by dividing 27 by 100 and multiplying by 1000 =

$\frac{27}{100} * 1000 = 270$ .

Finally, we are told 61% of respondents stated that they spend prime time hours in their dorm rooms. The actual number of students represented by the percentage is calculated by dividing 61 by 100 and multiplying by 1000 =

$\frac{61}{100} * 1000 = 610$

You might be interested in

If 2tanA=3tanB then prove that,<br>tan(A+B)= 5sin2B/5cos2B-1

Fed [463]

By definition of tangent,

tan(A + B) = sin(A + B) / cos(A + B)

Using the angle sum identities for sine and cosine,

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

yields

tan(A + B) = (sin(A) cos(B) + cos(A) sin(B)) / (cos(A) cos(B) - sin(A) sin(B))

Multiplying the right side by 1/(cos(A) cos(B)) uniformly gives

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) tan(B))

Since 2 tan(A) = 3 tan(B), it follows that

tan(A + B) = (3/2 tan(B) + tan(B)) / (1 - 3/2 tan²(B))

… = 5 tan(B) / (2 - 3 tan²(B))

Putting everything back in terms of sin and cos gives

tan(A + B) = (5 sin(B)/cos(B)) / (2 - 3 sin²(B)/cos²(B))

Multiplying uniformly by cos²(B) gives

tan(A + B) = 5 sin(B) cos(B) / (2 cos²(B) - 3 sin²(B))

Recall the double angle identities for sin and cos:

sin(2x) = 2 sin(x) cos(x)

cos(2x) = cos²(x) - sin²(x)

and multiplying uniformly by 2, we find that

tan(A + B) = 10 sin(B) cos(B) / (4 cos²(B) - 6 sin²(B))

… = 10 sin(B) cos(B) / (4 (cos²(B) - sin²(B)) - 2 sin²(B))

… = 5 sin(2B) / (4 cos(2B) - 2 sin²(B))

The Pythagorean identity,

cos²(x) + sin²(x) = 1

lets us rewrite the double angle identity for cos as

cos(2x) = 1 - 2 sin²(x)

so it follows that

tan(A + B) = 5 sin(2B) / (4 cos(2B) + 1 - 2 sin²(B) - 1)

… = 5 sin(2B) / (4 cos(2B) + cos(2B) - 1)

… = 5 sin(2B) / (4 cos(2B) - 1)

as required.

5 0

2 years ago

It’s on the picture .

Marrrta [24]

Answer:

slope 2

yint 1

equation y=2x+1

3 0

3 years ago

WORD PROBLEM! Sally has 15 apples. She gives some of her apples to three friends. They each get the same amount. Sally now has 9

Roman55 [17]

Answer:

Each friend got 2 apples

Step-by-step explanation:

[original amount of apples]-[Apples Sally has after distribution] = [friends] x [number of apples]

Filling in the brackets, you get this equation.

15-9=3 x apples per friend

6=3 x apples per friend

2 = apples per friend

5 0

3 years ago

Read 2 more answers

What is the value of sin theta in the diagram below?

Kay [80]

sin theta = opp/hyp

sin theta =y/r

sin theta = 24/25 /1

sin theta = 24/25

7 0

3 years ago

Read 2 more answers

What is (5/9×(°F-32))

djyliett [7]

Answer:

32º

Step-by-step explanation:

Fº-32 ×5/9

5/9Fº-160/9

5/9Fº =160/9

(5Fº)9=9(160)

45Fº=1440

divide both sides by 45

Fº=32

6 0

3 years ago